Question

Jace is making a water play table from a triangular table top. He sketched a dotted line to show where he wants to add a circular water bowl. It should go all the way to the edges of the table as shown.

A circle is inscribed within triangle A B C. The length of A B is 3.5 feet, the length of B C is 4 feet, and the length of A C is 2 feet. Angle A B C is 30 degrees and angle A C B is 60 degrees.
What should Jace do first to find the exact location of the center of the circular water bowl?

He should find the midpoint of each edge of the table.
He should bisect each of the angles at the vertices of the triangular table top.
He should draw perpendicular lines through any point along the edges of the table.
He should draw perpendicular line segments from each corner to the opposite edge of the table.

Answer 1

He should bisect each of the angles at the vertices of the triangular table top.

Reason: the incenter (center of the inscribed circle) is the intersection of the triangle's three angle bisectors; it is equidistant from all three sides and thus is the correct center for a circle tangent to every edge.